Revista Matemática Iberoamericana

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Volume 18, Issue 1, 2002, pp. 115–134
DOI: 10.4171/RMI/313

Published online: 2002-04-30

A uniform estimate for quartile operators

Christoph Thiele[1]

(1) Universität Bonn, Germany

There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove $L^p$ estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model: we prove the estimate $L^2\times L^2\to L^{1,\infty}$ uniformly for a discrete family of model operators for the bilinear Hilbert transform.

Keywords: Bilinear Hilbert Transform, Multilinear Singular Integrals, Uniform Estimates

Thiele Christoph: A uniform estimate for quartile operators. Rev. Mat. Iberoam. 18 (2002), 115-134. doi: 10.4171/RMI/313